32 candidates took examinations at centre. 11 took french,9 took spanish and x took both,18 took neither subject
1.Write an expression in x for the number of candidates in the universal set
2.Calculate the value of x
Use Venn diagrams
Draw two intersecting circles, label one French, the other Spanish
Place x in the overlap, 11-x in the non-overlapping part of the French circle and 9-x in the non-overlapping part of the Spanish circle. Put 18 outside the two circles.
11-x + x + 9-x + 18 = 32
solve for x=6
1. To find the number of candidates in the universal set, we need to consider the total number of candidates who took French, Spanish, or both. We can express this using the formula:
Total candidates in the universal set = Candidates who took French + Candidates who took Spanish - Candidates who took both + Candidates who took neither
Let's denote the number of candidates in the universal set as N. The expression for N would be:
N = 11 + 9 - x + 18
2. To calculate the value of x, we can use the given information:
Total candidates in the universal set = 32 (as mentioned in the question)
So, we can substitute this value into the equation:
32 = 11 + 9 - x + 18
Rearranging the equation, we have:
32 = 38 - x
Now, let's isolate x by subtracting 38 from both sides:
32 - 38 = -x
Simplifying further:
-6 = -x
To solve for x, we can multiply both sides by -1:
6 = x
Therefore, the value of x is 6.
To write an expression for the number of candidates in the universal set, we need to consider the candidates who took French, Spanish, and neither subject.
1. Expressing the number of candidates in the universal set:
The number of candidates who took only French subjects is given as 11. The number of candidates who took only Spanish subjects is given as 9. The number of candidates who took both French and Spanish is represented by 'x.' Finally, the number of candidates who took neither subject is given as 18.
To find the total number of candidates in the universal set, we need to add the number of candidates who took each subject. However, we need to be careful not to double-count the candidates who took both subjects. So, the expression for the number of candidates in the universal set (N) can be written as:
N = Candidates who took French only + Candidates who took Spanish only + Candidates who took both + Candidates who took neither
N = 11 + 9 + x + 18
Now let's move on to calculating the value of x.
2. Calculating the value of x:
We are given that the total number of candidates is 32.
Therefore, we will substitute the value of N as 32 into the expression we derived earlier:
32 = 11 + 9 + x + 18
Simplifying the equation, we get:
32 = 38 + x
To solve for x, we need to isolate it on one side of the equation. Subtracting 38 from both sides:
32 - 38 = x
-6 = x
Therefore, the value of x is -6.
It's important to note that the value of x seems negative, which indicates an error in the calculation or problem. In this case, since we cannot have a negative number of candidates who took both French and Spanish, it suggests a logical error in the problem.